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I hate to play the "teacher card" here, but I have to disagree with you. I think that for ~25% of students, Algebra II is legitimately out of their grasp by the end of high school. Some of them do not have the mental capacity to ever learn such material, but for others, because of differences in how they develop, they will not be able to meet the required "checkpoints" in middle school and high school to keep them on track to enroll in and successfully complete Algebra II by high school. That's not to say that they will never have the ability to understand it, it's just that that particular goal is not realistic and they way we push them along even if they don't understand prerequisite material is setting them up for failure.
I want to leave the issue of motivation aside for this discussion.
I don't agree. 25 percent is a very large number. And do I think the school should just push children through? Nope. I believe there should be generous use of the fail and repeat option. I don't like the grade inflation involved in schooling and I definitely would not like it if my child was pushed along without knowing material. Most countries are teaching material ahead of the US so I def don't think it is a genetic failing of the US kids, or a developmental problem at all. I think it is a L-A-Z-Y problem.
Saying that a full 25 percent are incapable of algebra developmentally is like me saying my big fat butt is due to a metabolic problem (it isn't BTW)
A classroom of 25-30 kids is a relatively small and almost certainly unrepresentative sample size. Because of how segregated (culturally, socioeconomically, etc.) our schools have become, you're absolutely right that oftentimes that aren't huge gaps between the top and bottom. However on a society-wide basis, the expectations we have may not (and in my opinion, do not) reflect the reality of what a huge chunk of our kids can actually learn and retain.
I hate to play the "teacher card" here, but I have to disagree with you. I think that for ~25% of students, Algebra II is legitimately out of their grasp by the end of high school. Some of them do not have the mental capacity to ever learn such material, but for others, because of differences in how they develop, they will not be able to meet the required "checkpoints" in middle school and high school to keep them on track to enroll in and successfully complete Algebra II by high school. That's not to say that they will never have the ability to understand it, it's just that that particular goal is not realistic and they way we push them along even if they don't understand prerequisite material is setting them up for failure.
I want to leave the issue of motivation aside for this discussion.
That's not what I meant. I have some experience with this percentile stuff, working as I do in a pediatric office. We do percentiles of height and weight. There's not a huge difference between 25 and 75, period.
I think the normal distribution applies in large groups. There's no telling the distribution in a classroom of 25-30 kids, though. Also (IMO), the range is really not as wide as it may sound. In other words, I don't think there's a HUGE difference between someone in the 25th percentile and someone in the 75th. Take note of word in bold, caps.
There's not much of a difference between an IQ of 70 and an IQ of 80 but an IQ of 70 can get you labelled mentally deficient.
I don't agree. 25 percent is a very large number. And do I think the school should just push children through? Nope. I believe there should be generous use of the fail and repeat option. I don't like the grade inflation involved in schooling and I definitely would not like it if my child was pushed along without knowing material. Most countries are teaching material ahead of the US so I def don't think it is a genetic failing of the US kids, or a developmental problem at all. I think it is a L-A-Z-Y problem.
Saying that a full 25 percent are incapable of algebra developmentally is like me saying my big fat butt is due to a metabolic problem (it isn't BTW)
But is it really true that the vast majority of students in other Western countries are mastering Algebra II or higher by the end of high school? I don't know if that's really the case. This goal of "Algebra II for all" is, as far as I can tell, an arbitrary expectation that may or may not be realistically attainable. It sounds good on paper to say that we want everyone to master Algebra II, but I'm not sure that there's any real research that says that it's attainable by more than 75% of the population (and I'm pulling that 75% number based on anecdotes; that may even be a reach itself).
And again, while it's true that motivation is a problem in this country, even if all students were perfectly motivated a huge chunk of them would not have the mental capacity to reach whatever arbitrary level of achievement that the government set. What percentage would be dependent on what level society expected. In this case, I think that Algebra II is a pretty high bar.
That's not what I meant. I have some experience with this percentile stuff, working as I do in a pediatric office. We do percentiles of height and weight. There's not a huge difference between 25 and 75, period.
My point was that students in certain schools are very likely clustered around the 25th percentile and certain schools are clustered more around the 75th percentile. But in reality I'm not sure that line of discussion matters; it's possible that we have set expectations that may be a stretch now for even that middle 68%, I'm not sure. However I am fairly certain based on experience that our expectations are much too high for those more than 1 SD away from the mean (roughly 15% of students).
My point was that students in certain schools are very likely clustered around the 25th percentile and certain schools are clustered more around the 75th percentile. But in reality I'm not sure that line of discussion matters; it's possible that we have set expectations that may be a stretch now for even that middle 68%, I'm not sure. However I am fairly certain based on experience that our expectations are much too high for those more than 1 SD away from the mean (roughly 15% of students).
I seriously doubt it, but there's no way to prove either one of us is right.
Does the Normal Distribution Apply to Student Ability/Intelligence?
Of course it does. But that won't do much to change the great misconception that "Americans are all above average" that seems to be so widespread among the public. Witness the current flavor-of-the-month approach in US education: all kids are college material.
I seriously doubt it, but there's no way to prove either one of us is right.
What makes you doubt it?
In terms of supporting my claim, think about average SAT* scores by school. Are these evenly distributed like we would expect to see if students were randomly dispersed by intelligence? Nope. There are schools where clusters of high (and low) scores exist that are certainly indicative of something going on that is not a chance process. There are forces at play that have brought us to this situation, but the point is that in my opinion schools are not all dealing with populations that have a representative spectrum of student intelligence; there are schools where high intelligent students are clustered and there are schools were lower intelligence students are clustered.
To take it to another extremely nerdy level, if all students were randomly assigned schools and parents did not purposefully cluster in certain areas where schools are perceived to be better, then a graph of the average IQ of schools itself would form a normal distribution. Can you envision that being the case?
*SAT scores correlate fairly closely with IQ scores, so I think that's a safe though imperfect measure of average intelligence of a given high school population. There are problems with this, but it adequately serves its purpose for this illustration I believe.
But is it really true that the vast majority of students in other Western countries are mastering Algebra II or higher by the end of high school? I don't know if that's really the case. This goal of "Algebra II for all" is, as far as I can tell, an arbitrary expectation that may or may not be realistically attainable. It sounds good on paper to say that we want everyone to master Algebra II, but I'm not sure that there's any real research that says that it's attainable by more than 75% of the population (and I'm pulling that 75% number based on anecdotes; that may even be a reach itself).
And again, while it's true that motivation is a problem in this country, even if all students were perfectly motivated a huge chunk of them would not have the mental capacity to reach whatever arbitrary level of achievement that the government set. What percentage would be dependent on what level society expected. In this case, I think that Algebra II is a pretty high bar.
My friend (an average student in Japan) came to the US in 8th grade and did not have to learn any new subject matter in math for two years. You are seriously underestimating capability. As for percentages/ex. who takes what math in what country- No need to argue those stats-those are quite easy to discover with a little digging.
My friend (an average student in Japan) came to the US in 8th grade and did not have to learn any new subject matter in math for two years. You are seriously underestimating capability. As for percentages/ex. who takes what math in what country- No need to argue those stats-those are quite easy to discover with a little digging.
Anecdotes aren't all that helpful here. More than a few Japanese (and other Asian) immigrants come to this country and are successful academically. Some of this undoubtedly has to do with self-selection and the type of person that is likely to immigrate here. And some of it may have to do with something else that people don't like to discuss.
The United States is one of the most heterogeneous Western countries which I think makes comparison to other countries very difficult on such measures.
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Does the Normal Distribution Apply to Student Ability/Intelligence?
